The New Equation Deduces the Counting Formula of Repeatable Combination under Arbitrary Conditions

2019 ◽  
Vol 08 (09) ◽  
pp. 1556-1561
Author(s):  
友谊 黄
2019 ◽  
Author(s):  
Vitaly Kuyukov

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.


Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 611
Author(s):  
Yeon-Woong Choe ◽  
Sang-Bo Sim ◽  
Yeon-Moon Choo

In general, this new equation is significant for designing and operating a pipeline to predict flow discharge. In order to predict the flow discharge, accurate determination of the flow loss due to pipe friction is very important. However, existing pipe friction coefficient equations have difficulties in obtaining key variables or those only applicable to pipes with specific conditions. Thus, this study develops a new equation for predicting pipe friction coefficients using statistically based entropy concepts, which are currently being used in various fields. The parameters in the proposed equation can be easily obtained and are easy to estimate. Existing formulas for calculating pipe friction coefficient requires the friction head loss and Reynolds number. Unlike existing formulas, the proposed equation only requires pipe specifications, entropy value and average velocity. The developed equation can predict the friction coefficient by using the well-known entropy, the mean velocity and the pipe specifications. The comparison results with the Nikuradse’s experimental data show that the R2 and RMSE values were 0.998 and 0.000366 in smooth pipe, and 0.979 to 0.994 or 0.000399 to 0.000436 in rough pipe, and the discrepancy ratio analysis results show that the accuracy of both results in smooth and rough pipes is very close to zero. The proposed equation will enable the easier estimation of flow rates.


Author(s):  
Lorenzo Giosa ◽  
Mattia Busana ◽  
Iacopo Pasticci ◽  
Matteo Bonifazi ◽  
Matteo Maria Macrì ◽  
...  

Abstract Background Mechanical power is a summary variable including all the components which can possibly cause VILI (pressures, volume, flow, respiratory rate). Since the complexity of its mathematical computation is one of the major factors that delay its clinical use, we propose here a simple and easy to remember equation to estimate mechanical power under volume-controlled ventilation: $$ \mathrm{Mechanical}\ \mathrm{Power}=\frac{\mathrm{VE}\times \left(\mathrm{Peak}\ \mathrm{Pressure}+\mathrm{PEEP}+F/6\right)}{20} $$Mechanical Power=VE×Peak Pressure+PEEP+F/620 where the mechanical power is expressed in Joules/minute, the minute ventilation (VE) in liters/minute, the inspiratory flow (F) in liters/minute, and peak pressure and positive end-expiratory pressure (PEEP) in centimeter of water. All the components of this equation are continuously displayed by any ventilator under volume-controlled ventilation without the need for clinician intervention. To test the accuracy of this new equation, we compared it with the reference formula of mechanical power that we proposed for volume-controlled ventilation in the past. The comparisons were made in a cohort of mechanically ventilated pigs (485 observations) and in a cohort of ICU patients (265 observations). Results Both in pigs and in ICU patients, the correlation between our equation and the reference one was close to the identity. Indeed, the R2 ranged from 0.97 to 0.99 and the Bland-Altman showed small biases (ranging from + 0.35 to − 0.53 J/min) and proportional errors (ranging from + 0.02 to − 0.05). Conclusions Our new equation of mechanical power for volume-controlled ventilation represents a simple and accurate alternative to the more complex ones available to date. This equation does not need any clinical intervention on the ventilator (such as an inspiratory hold) and could be easily implemented in the software of any ventilator in volume-controlled mode. This would allow the clinician to have an estimation of mechanical power at a simple glance and thus increase the clinical consciousness of this variable which is still far from being used at the bedside. Our equation carries the same limitations of all other formulas of mechanical power, the most important of which, as far as it concerns VILI prevention, are the lack of normalization and its application to the whole respiratory system (including the chest wall) and not only to the lung parenchyma.


2001 ◽  
Vol 15 (03) ◽  
pp. 105-109
Author(s):  
M. S. HUSSEIN

We derive a generalized Low equation for the T-matrix appropriate for complex atom–molecule interaction. The properties of this new equation at very low energies are studied and the complex scattering length and effective range are derived.


2021 ◽  
Vol 13 (10) ◽  
pp. 5355
Author(s):  
Vilém Pechanec ◽  
Ondřej Cudlín ◽  
Miloš Zapletal ◽  
Jan Purkyt ◽  
Lenka Štěrbová ◽  
...  

Global and regional biodiversity loss is caused by several drivers including urban development, land use intensification, overexploitation of natural resources, environmental pollution, and climate change. The main aim of our study was to adapt the GLOBIO3 model to the conditions of the Czech Republic (CR) to assess loss of naturalness and biodiversity vulnerability at the habitat level on a detailed scale across the entire CR. An additional aim was to assess the main drivers affecting the biodiversity of habitat types. The GLOBIO3 model was adapted to CZ-GLOBIO by adapting global to local scales and using habitat quality and naturalness data instead of species occurrence data. The total mean species abundance (MSA) index of habitat quality, calculated from the spatial overlay of the four MSA indicators by our new equation, reached the value 0.62. The total value of MSA for natural and near-natural habitats was found to be affected mainly by infrastructure development and fragmentation. Simultaneously, intensity of land use change and atmospheric nitrogen deposition contributed primarily to the low total value of MSA for distant natural habitats. The CZ-GLOBIO model can be an important tool in political decision making to reduce the impact of the main drivers on habitat biodiversity in the CR.


2021 ◽  
Vol 40 (S1) ◽  
Author(s):  
Fatimah Othman ◽  
Rashidah Ambak ◽  
Mohd Azahadi Omar ◽  
Suzana Shahar ◽  
Noor Safiza Mohd Nor ◽  
...  

Abstract Background Monitoring sodium intake through 24-h urine collection sample is recommended, but the implementation of this method can be difficult. The objective of this study was to develop and validate an equation using spot urine concentration to predict 24-h sodium excretion in the Malaysian population. Methods This was a Malaysian Community Salt Study (MyCoSS) sub-study, which was conducted from October 2017 to March 2018. Out of 798 participants in the MyCoSS study who completed 24-h urine collection, 768 of them have collected one-time spot urine the following morning. They were randomly assigned into two groups to form separate spot urine equations. The final spot urine equation was derived from the entire data set after confirming the stability of the equation by double cross-validation in both study groups. Newly derived spot urine equation was developed using the coefficients from the multiple linear regression test. A Bland-Altman plot was used to measure the mean bias and limits of agreement between estimated and measured 24-h urine sodium. The estimation of sodium intake using the new equation was compared with other established equations, namely Tanaka and INTERSALT. Results The new equation showed the least mean bias between measured and predicted sodium, − 0.35 (− 72.26, 71.56) mg/day compared to Tanaka, 629.83 (532.19, 727.47) mg/day and INTERSALT, and 360.82 (284.34, 437.29) mg/day. Predicted sodium measured from the new equation showed greater correlation with measured sodium (r = 0.50) compared to Tanaka (r =0.24) and INTERSALT (r = 0.44), P < 0.05. Conclusion Our newly developed equation from spot urine can predict least mean bias of sodium intake among the Malaysian population when 24-h urine sodium collection is not feasible.


Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.


2021 ◽  
Vol 64 (3) ◽  
pp. 470-493 ◽  
Author(s):  
Jianping Chen ◽  
Xulong Wang ◽  
Jianfa Chen ◽  
Yunyan Ni ◽  
Baoli Xiang ◽  
...  

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